Totally flat foliations and peakless functions
type: Item
instance of: scholarly article
title: Totally flat foliations and peakless functions
zbMATH Open document ID: 0554.53045
DOI: 10.1007/BF01207575
author: Nobuhiro Innami
published in: Archiv der Mathematik
publication date: 1983-01-01T00:00:00Z
review text: A continuous function is peakless if it is monotone on each geodesic except possibly on an interval where it attains a minimum. Suppose in addition the function goes to infinity in any direction in which it is increasing. Let \(\{f_ i\}\) be a sequence of functions on a noncompact space satisfying the above conditions, and such that for some constants \(\{a_ i\}\), the sets where \(f_ i\leq a_ i\) are pairwise disjoint and the complement of their union is bounded. Then the space has exactly two ends, defined by two suitably chosen functions of the sequence, and the boundaries of the sets where \(f_ i\leq a_ i\) define a totally geodesic foliation of part of the space. The result is obtained in the context of G-spaces, and assumes no differentiability.
Mathematics Subject Classification ID: 53C70
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 3883163
zbMATH Keywords: peakless function
zbMATH Keywords: totally geodesic foliation
zbMATH Keywords: G-spaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3883163